What is the difference between align and equation environments?

The equation environment is for single-line equations with one number. The align environment handles multiple lines with alignment points marked by ampersand symbols. Use align when you have multi-line derivations or want to align equals signs across related equations.

How do I number only some equations in a multi-line block?

Use the align environment and add nonumber before the line break on lines you do not want numbered. Alternatively, use align* for no numbers at all. The split environment inside equation gives one number for multiple lines.

What packages do I need for advanced math typesetting?

Load amsmath as your foundation for enhanced environments like align, gather, and cases. Add amssymb for additional symbols. The mathtools package extends amsmath with useful features like better delimiters and dcases. These three packages cover most advanced math needs.

How do I create a piecewise function with cases in LaTeX?

Use the cases environment inside an equation. Each line has the expression, an ampersand, then the condition with text command for words. End lines with double backslash. For better spacing with fractions, use dcases from the mathtools package instead.

Advanced LaTeX Math: Multi-Line Equations, Alignment, and Custom Notation

Your Equations Can Look Like a Textbook

You've seen papers where the mathematics is beautiful. Multi-line derivations that flow naturally. Perfectly aligned equals signs. Custom operators that match the surrounding text. Equation numbering that makes sense.

Then you look at your own LaTeX—a mess of equation environments and manual spacing.

The difference isn't talent. It's knowing the right techniques. Let's go beyond $x^2$ and \frac{}{} into the advanced formatting that makes complex mathematics readable. (Need to find a specific symbol? Try our symbol finder.)

The AMS Packages

For serious math typesetting, load the AMS packages:

\usepackage{amsmath}   % Core math enhancements
\usepackage{amssymb}   % Additional symbols
\usepackage{amsthm}    % Theorem environments
\usepackage{mathtools} % Extensions to amsmath

amsmath is essential. The others add useful extensions.

Multi-Line Equations

The align Environment

For equations with alignment points:

\begin{align}
    f(x) &= x^2 + 2x + 1 \\
         &= (x + 1)^2
\end{align}

The & marks alignment points. Use \\ for line breaks.

Multiple Alignment Points

\begin{align}
    a &= b + c    &\quad d &= e + f \\
    g &= h        &\quad i &= j + k + l
\end{align}

This creates two columns of aligned equations.

Unnumbered Equations

% No numbers at all
\begin{align*}
    y &= mx + b \\
      &= 2x + 3
\end{align*}
 
% Selective numbering
\begin{align}
    y &= mx + b \nonumber \\
      &= 2x + 3
\end{align}

The gather Environment

For centered equations without alignment:

\begin{gather}
    E = mc^2 \\
    F = ma \\
    PV = nRT
\end{gather}

Equation Groups

The subequations Environment

For labeling related equations:

\begin{subequations}
\label{eq:maxwell}
\begin{align}
    \nabla \cdot \mathbf{E} &= \frac{\rho}{\epsilon_0} \label{eq:maxwell-gauss} \\
    \nabla \cdot \mathbf{B} &= 0 \label{eq:maxwell-divb} \\
    \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \label{eq:maxwell-faraday} \\
    \nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \label{eq:maxwell-ampere}
\end{align}
\end{subequations}

This produces equations (1a), (1b), (1c), (1d).

The split Environment

For a single equation number across multiple lines:

\begin{equation}
\begin{split}
    f(x) &= a + b + c + d \\
         &\quad + e + f + g \\
         &= \text{result}
\end{split}
\end{equation}

One equation number for all lines.

Conditional Expressions

Cases

\begin{equation}
    f(x) = \begin{cases}
        x^2 & \text{if } x \geq 0 \\
        -x & \text{if } x < 0
    \end{cases}
\end{equation}

More Complex Conditions

\begin{equation}
    \delta_{ij} = \begin{cases}
        1 & \text{if } i = j \\
        0 & \text{otherwise}
    \end{cases}
\end{equation}

dcases for Better Spacing

From mathtools:

\usepackage{mathtools}
 
\begin{equation}
    f(x) = \begin{dcases}
        \frac{x^2}{2} & \text{if } x \geq 0 \\
        \frac{-x}{2} & \text{if } x < 0
    \end{dcases}
\end{equation}

dcases uses display-style fractions inside cases.

Matrices

Basic Matrices

\begin{equation}
    A = \begin{pmatrix}
        a & b \\
        c & d
    \end{pmatrix}
\end{equation}

Matrix Types

% Parentheses
\begin{pmatrix} a & b \\ c & d \end{pmatrix}
 
% Brackets
\begin{bmatrix} a & b \\ c & d \end{bmatrix}
 
% Braces
\begin{Bmatrix} a & b \\ c & d \end{Bmatrix}
 
% Vertical bars (determinant)
\begin{vmatrix} a & b \\ c & d \end{vmatrix}
 
% Double vertical bars
\begin{Vmatrix} a & b \\ c & d \end{Vmatrix}
 
% No delimiters
\begin{matrix} a & b \\ c & d \end{matrix}

Small Matrices

For inline use:

The matrix $\begin{psmallmatrix} a & b \\ c & d \end{psmallmatrix}$
is invertible.

Large Matrices with Ellipses

\begin{equation}
    A = \begin{pmatrix}
        a_{11} & a_{12} & \cdots & a_{1n} \\
        a_{21} & a_{22} & \cdots & a_{2n} \\
        \vdots & \vdots & \ddots & \vdots \\
        a_{m1} & a_{m2} & \cdots & a_{mn}
    \end{pmatrix}
\end{equation}

Custom Operators

Defining Operators

% Simple operator
\DeclareMathOperator{\argmax}{arg\,max}
\DeclareMathOperator{\argmin}{arg\,min}
\DeclareMathOperator{\tr}{tr}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\rank}{rank}
 
% With limits (like \lim)
\DeclareMathOperator*{\argmax}{arg\,max}

Usage:

\begin{equation}
    \hat{\theta} = \argmax_\theta \mathcal{L}(\theta)
\end{equation}

Common Custom Operators

\DeclareMathOperator{\sgn}{sgn}      % Sign function
\DeclareMathOperator{\sinc}{sinc}    % Sinc function
\DeclareMathOperator{\Var}{Var}      % Variance
\DeclareMathOperator{\Cov}{Cov}      % Covariance
\DeclareMathOperator{\E}{\mathbb{E}} % Expectation

Delimiters

Automatic Sizing

% Automatic sizing
\left( \frac{a}{b} \right)
\left[ \sum_{i=1}^n x_i \right]
\left\{ \int_0^\infty f(x)\,dx \right\}
 
% Manual sizing
\bigl( \Bigl( \biggl( \Biggl(
\bigr) \Bigr) \biggr) \Biggr)

Mixed Delimiters

\left. \frac{df}{dx} \right|_{x=0}  % Right bar only
 
\left( x + y \right.               % Left paren, nothing right

Absolute Value and Norms

\usepackage{mathtools}
 
\DeclarePairedDelimiter\abs{\lvert}{\rvert}
\DeclarePairedDelimiter\norm{\lVert}{\rVert}
 
% Usage:
\abs{x}       % |x|
\abs*{\frac{a}{b}}  % Auto-sized
\norm{v}      % ||v||

Spacing Control

Standard Spaces

a\,b      % Thin space (6/18 quad)
a\:b      % Medium space (4/18 quad)
a\;b      % Thick space (5/18 quad)
a\quad b  % Full quad
a\qquad b % Double quad
a\ b      % Normal text space
a\! b     % Negative thin space

In Practice

% Integral spacing
\int f(x) \, dx     % Thin space before dx
 
% Function notation
\sin x              % sin x (correct)
sin x               % Wrong: si n x
 
% Abbreviations
\text{s.t.}\quad x > 0  % "such that"

Text in Equations

The text Command

\begin{equation}
    x = y \quad \text{if and only if} \quad y = x
\end{equation}

The intertext Command

\begin{align}
    a &= b + c \\
    \intertext{Substituting the expression for $b$:}
    a &= (d + e) + c \\
      &= d + e + c
\end{align}

Short Intertext

\begin{align}
    x &= y \\
    \shortintertext{and}
    z &= w
\end{align}

Advanced Techniques

Phantom for Alignment

\begin{align}
    x + y &= 10 \\
    \phantom{x +{}} y &= 3  % Align the y's
\end{align}

Overlapping Notation

% Stack symbols
\overset{?}{=}          % =? above
\underset{\text{def}}{=}  % def below
\stackrel{\text{def}}{=}  % Alternative
 
% Overbrace and underbrace
\underbrace{a + b + c}_{3 \text{ terms}}
\overbrace{x_1 + x_2 + \cdots + x_n}^{n \text{ terms}}

Boxed Equations

\begin{equation}
    \boxed{E = mc^2}
\end{equation}

Colored Equations

\usepackage{xcolor}
 
\begin{equation}
    y = \textcolor{blue}{ax^2} + \textcolor{red}{bx} + c
\end{equation}

Common Symbols

Greek Letters

% Variants
\epsilon, \varepsilon    % ε, ε
\theta, \vartheta        % θ, ϑ
\phi, \varphi            % φ, ϕ
\pi, \varpi              % π, ϖ
\rho, \varrho            % ρ, ϱ

Arrows

\rightarrow, \to         % →
\leftarrow, \gets        % ←
\Rightarrow, \Implies    % ⇒
\Leftarrow               % ⇐
\Leftrightarrow, \iff    % ⇔
\mapsto                  % ↦
\hookrightarrow          % ↪

Relations

\leq, \geq               % ≤, ≥
\ll, \gg                 % ≪, ≫
\approx, \sim            % ≈, ∼
\equiv                   % ≡
\propto                  % ∝
\neq                     % ≠
\in, \notin              % ∈, ∉
\subset, \supset         % ⊂, ⊃
\subseteq, \supseteq     % ⊆, ⊇

Big Operators

\sum_{i=1}^n             % Summation
\prod_{i=1}^n            % Product
\int_a^b                 % Integral
\oint                    % Contour integral
\iint, \iiint            % Multiple integrals
\bigcup, \bigcap         % Set operations

Troubleshooting

Common Issues

Equation too wide:

% Use split or multline
\begin{multline}
    a + b + c + d + e + f + g \\
    = h + i + j + k
\end{multline}

Poor fraction rendering:

% In text, use \tfrac for small fractions
The ratio is $\tfrac{1}{2}$.
 
% In display, \dfrac forces display style
$\dfrac{a}{b}$

Inconsistent operator spacing:

% Always use \DeclareMathOperator for functions
\DeclareMathOperator{\myop}{myop}
% Not: $myop$ or $\mathrm{myop}$

Quick Reference

Environment Summary

| Environment | Use For | |-------------|---------| | equation | Single numbered equation | | equation* | Single unnumbered equation | | align | Multiple aligned equations | | gather | Multiple centered equations | | multline | Single long equation | | split | Multi-line, one number | | cases | Conditional expressions |

Useful Commands

% Fractions
\frac{a}{b}, \tfrac{a}{b}, \dfrac{a}{b}
 
% Roots
\sqrt{x}, \sqrt[n]{x}
 
% Over/under
\hat{x}, \bar{x}, \vec{v}, \tilde{x}
\dot{x}, \ddot{x}
\overline{abc}, \underline{abc}
 
% Big operators with limits
\sum_{i=1}^n, \prod, \int, \oint

Conclusion

Advanced math typesetting requires knowing the right environments and commands. Master align for multi-line equations, cases for conditionals, and mathtools for enhanced delimiters—these cover most needs.

The key principles:

Use AMS packages
Align at meaningful points
Control numbering intentionally
Define custom operators for consistency
Let LaTeX handle spacing (mostly)

With these tools, you can typeset any mathematical notation beautifully.

Your Equations Can Look Like a Textbook

Then you look at your own LaTeX—a mess of equation environments and manual spacing.

The AMS Packages

For serious math typesetting, load the AMS packages:

\usepackage{amsmath}   % Core math enhancements
\usepackage{amssymb}   % Additional symbols
\usepackage{amsthm}    % Theorem environments
\usepackage{mathtools} % Extensions to amsmath

amsmath is essential. The others add useful extensions.

Multi-Line Equations

The align Environment

For equations with alignment points:

\begin{align}
    f(x) &= x^2 + 2x + 1 \\
         &= (x + 1)^2
\end{align}

The & marks alignment points. Use \\ for line breaks.

Multiple Alignment Points

\begin{align}
    a &= b + c    &\quad d &= e + f \\
    g &= h        &\quad i &= j + k + l
\end{align}

This creates two columns of aligned equations.

Unnumbered Equations

% No numbers at all
\begin{align*}
    y &= mx + b \\
      &= 2x + 3
\end{align*}
 
% Selective numbering
\begin{align}
    y &= mx + b \nonumber \\
      &= 2x + 3
\end{align}

The gather Environment

For centered equations without alignment:

\begin{gather}
    E = mc^2 \\
    F = ma \\
    PV = nRT
\end{gather}

Equation Groups

The subequations Environment

For labeling related equations:

\begin{subequations}
\label{eq:maxwell}
\begin{align}
    \nabla \cdot \mathbf{E} &= \frac{\rho}{\epsilon_0} \label{eq:maxwell-gauss} \\
    \nabla \cdot \mathbf{B} &= 0 \label{eq:maxwell-divb} \\
    \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \label{eq:maxwell-faraday} \\
    \nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \label{eq:maxwell-ampere}
\end{align}
\end{subequations}

This produces equations (1a), (1b), (1c), (1d).

The split Environment

For a single equation number across multiple lines:

\begin{equation}
\begin{split}
    f(x) &= a + b + c + d \\
         &\quad + e + f + g \\
         &= \text{result}
\end{split}
\end{equation}

One equation number for all lines.

Conditional Expressions

Cases

\begin{equation}
    f(x) = \begin{cases}
        x^2 & \text{if } x \geq 0 \\
        -x & \text{if } x < 0
    \end{cases}
\end{equation}

More Complex Conditions

\begin{equation}
    \delta_{ij} = \begin{cases}
        1 & \text{if } i = j \\
        0 & \text{otherwise}
    \end{cases}
\end{equation}

dcases for Better Spacing

From mathtools:

\usepackage{mathtools}
 
\begin{equation}
    f(x) = \begin{dcases}
        \frac{x^2}{2} & \text{if } x \geq 0 \\
        \frac{-x}{2} & \text{if } x < 0
    \end{dcases}
\end{equation}

dcases uses display-style fractions inside cases.

Matrices

Basic Matrices

\begin{equation}
    A = \begin{pmatrix}
        a & b \\
        c & d
    \end{pmatrix}
\end{equation}

Matrix Types

% Parentheses
\begin{pmatrix} a & b \\ c & d \end{pmatrix}
 
% Brackets
\begin{bmatrix} a & b \\ c & d \end{bmatrix}
 
% Braces
\begin{Bmatrix} a & b \\ c & d \end{Bmatrix}
 
% Vertical bars (determinant)
\begin{vmatrix} a & b \\ c & d \end{vmatrix}
 
% Double vertical bars
\begin{Vmatrix} a & b \\ c & d \end{Vmatrix}
 
% No delimiters
\begin{matrix} a & b \\ c & d \end{matrix}

Small Matrices

For inline use:

The matrix $\begin{psmallmatrix} a & b \\ c & d \end{psmallmatrix}$
is invertible.

Large Matrices with Ellipses

\begin{equation}
    A = \begin{pmatrix}
        a_{11} & a_{12} & \cdots & a_{1n} \\
        a_{21} & a_{22} & \cdots & a_{2n} \\
        \vdots & \vdots & \ddots & \vdots \\
        a_{m1} & a_{m2} & \cdots & a_{mn}
    \end{pmatrix}
\end{equation}

Custom Operators

Defining Operators

% Simple operator
\DeclareMathOperator{\argmax}{arg\,max}
\DeclareMathOperator{\argmin}{arg\,min}
\DeclareMathOperator{\tr}{tr}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\rank}{rank}
 
% With limits (like \lim)
\DeclareMathOperator*{\argmax}{arg\,max}

Usage:

\begin{equation}
    \hat{\theta} = \argmax_\theta \mathcal{L}(\theta)
\end{equation}

Common Custom Operators

\DeclareMathOperator{\sgn}{sgn}      % Sign function
\DeclareMathOperator{\sinc}{sinc}    % Sinc function
\DeclareMathOperator{\Var}{Var}      % Variance
\DeclareMathOperator{\Cov}{Cov}      % Covariance
\DeclareMathOperator{\E}{\mathbb{E}} % Expectation

Delimiters

Automatic Sizing

% Automatic sizing
\left( \frac{a}{b} \right)
\left[ \sum_{i=1}^n x_i \right]
\left\{ \int_0^\infty f(x)\,dx \right\}
 
% Manual sizing
\bigl( \Bigl( \biggl( \Biggl(
\bigr) \Bigr) \biggr) \Biggr)

Mixed Delimiters

\left. \frac{df}{dx} \right|_{x=0}  % Right bar only
 
\left( x + y \right.               % Left paren, nothing right

Absolute Value and Norms

\usepackage{mathtools}
 
\DeclarePairedDelimiter\abs{\lvert}{\rvert}
\DeclarePairedDelimiter\norm{\lVert}{\rVert}
 
% Usage:
\abs{x}       % |x|
\abs*{\frac{a}{b}}  % Auto-sized
\norm{v}      % ||v||

Spacing Control

Standard Spaces

a\,b      % Thin space (6/18 quad)
a\:b      % Medium space (4/18 quad)
a\;b      % Thick space (5/18 quad)
a\quad b  % Full quad
a\qquad b % Double quad
a\ b      % Normal text space
a\! b     % Negative thin space

In Practice

% Integral spacing
\int f(x) \, dx     % Thin space before dx
 
% Function notation
\sin x              % sin x (correct)
sin x               % Wrong: si n x
 
% Abbreviations
\text{s.t.}\quad x > 0  % "such that"

Text in Equations

The text Command

\begin{equation}
    x = y \quad \text{if and only if} \quad y = x
\end{equation}

The intertext Command

\begin{align}
    a &= b + c \\
    \intertext{Substituting the expression for $b$:}
    a &= (d + e) + c \\
      &= d + e + c
\end{align}

Short Intertext

\begin{align}
    x &= y \\
    \shortintertext{and}
    z &= w
\end{align}

Advanced Techniques

Phantom for Alignment

\begin{align}
    x + y &= 10 \\
    \phantom{x +{}} y &= 3  % Align the y's
\end{align}

Overlapping Notation

% Stack symbols
\overset{?}{=}          % =? above
\underset{\text{def}}{=}  % def below
\stackrel{\text{def}}{=}  % Alternative
 
% Overbrace and underbrace
\underbrace{a + b + c}_{3 \text{ terms}}
\overbrace{x_1 + x_2 + \cdots + x_n}^{n \text{ terms}}

Boxed Equations

\begin{equation}
    \boxed{E = mc^2}
\end{equation}

Colored Equations

\usepackage{xcolor}
 
\begin{equation}
    y = \textcolor{blue}{ax^2} + \textcolor{red}{bx} + c
\end{equation}

Common Symbols

Greek Letters

% Variants
\epsilon, \varepsilon    % ε, ε
\theta, \vartheta        % θ, ϑ
\phi, \varphi            % φ, ϕ
\pi, \varpi              % π, ϖ
\rho, \varrho            % ρ, ϱ

Arrows

\rightarrow, \to         % →
\leftarrow, \gets        % ←
\Rightarrow, \Implies    % ⇒
\Leftarrow               % ⇐
\Leftrightarrow, \iff    % ⇔
\mapsto                  % ↦
\hookrightarrow          % ↪

Relations

\leq, \geq               % ≤, ≥
\ll, \gg                 % ≪, ≫
\approx, \sim            % ≈, ∼
\equiv                   % ≡
\propto                  % ∝
\neq                     % ≠
\in, \notin              % ∈, ∉
\subset, \supset         % ⊂, ⊃
\subseteq, \supseteq     % ⊆, ⊇

Big Operators

\sum_{i=1}^n             % Summation
\prod_{i=1}^n            % Product
\int_a^b                 % Integral
\oint                    % Contour integral
\iint, \iiint            % Multiple integrals
\bigcup, \bigcap         % Set operations

Troubleshooting

Common Issues

Equation too wide:

% Use split or multline
\begin{multline}
    a + b + c + d + e + f + g \\
    = h + i + j + k
\end{multline}

Poor fraction rendering:

% In text, use \tfrac for small fractions
The ratio is $\tfrac{1}{2}$.
 
% In display, \dfrac forces display style
$\dfrac{a}{b}$

Inconsistent operator spacing:

% Always use \DeclareMathOperator for functions
\DeclareMathOperator{\myop}{myop}
% Not: $myop$ or $\mathrm{myop}$

Quick Reference

Environment Summary

Useful Commands

% Fractions
\frac{a}{b}, \tfrac{a}{b}, \dfrac{a}{b}
 
% Roots
\sqrt{x}, \sqrt[n]{x}
 
% Over/under
\hat{x}, \bar{x}, \vec{v}, \tilde{x}
\dot{x}, \ddot{x}
\overline{abc}, \underline{abc}
 
% Big operators with limits
\sum_{i=1}^n, \prod, \int, \oint

Conclusion

The key principles:

Use AMS packages
Align at meaningful points
Control numbering intentionally
Define custom operators for consistency
Let LaTeX handle spacing (mostly)

With these tools, you can typeset any mathematical notation beautifully.

Your Equations Can Look Like a Textbook

The AMS Packages

Multi-Line Equations

The align Environment

Multiple Alignment Points

Unnumbered Equations

The gather Environment

Equation Groups

The subequations Environment

The split Environment

Conditional Expressions

Cases

More Complex Conditions

dcases for Better Spacing

Matrices

Basic Matrices

Matrix Types

Small Matrices

Large Matrices with Ellipses

Custom Operators

Defining Operators

Common Custom Operators

Delimiters

Automatic Sizing

Mixed Delimiters

Absolute Value and Norms

Spacing Control

Standard Spaces

In Practice

Text in Equations

The text Command

The intertext Command

Short Intertext

Advanced Techniques

Phantom for Alignment

Overlapping Notation

Boxed Equations

Colored Equations

Common Symbols

Greek Letters

Arrows

Relations

Big Operators

Troubleshooting

Common Issues

Quick Reference

Environment Summary

Useful Commands

Conclusion

Frequently Asked Questions

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Your Equations Can Look Like a Textbook

The AMS Packages

Multi-Line Equations

The align Environment

Multiple Alignment Points

Unnumbered Equations

The gather Environment

Equation Groups

The subequations Environment

The split Environment

Conditional Expressions

Cases

More Complex Conditions

dcases for Better Spacing

Matrices

Basic Matrices

Matrix Types

Small Matrices

Large Matrices with Ellipses

Custom Operators

Defining Operators

Common Custom Operators

Delimiters

Automatic Sizing

Mixed Delimiters

Absolute Value and Norms